v79b01.pdf - JSS Journal of Statistical Software July 2017...

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JSS Journal of Statistical Software July 2017, Volume 79, Book Review 1. doi: 10.18637/jss.v079.b01 Reviewer: Hakan Demirtas University of Illinois at Chicago Bayesian Computation with R (2nd Edition) Jim Albert Springer-Verlag, New York, 2009. ISBN 978-0387922973978. xii + 300 pp. USD 59.95 (P). The new material added in the 2nd edition include the mixture of conjugate priors, the use of the SIR (sampling importance resampling) to explore the sensitivity of Bayesian inferences with respect to changes in the prior, and Zellner’s g priors to choose between models in linear regression. Chapter 1 is allocated to basic data manipulations and rudimentary analysis in R . The highlight of the chapter is a simulation study about the true significance levels com- puted by Monte Carlo experiments. Chapter 2 introduces the basic elements of the Bayesian inferential approach. Forming the posterior distribution via prior distribution and likelihood, obtaining summaries of this probability distribution as well as predicting the likely outcomes of a new sample are described in an intuitively appealing manner. Chapters 3 and 4 illustrate the use of R for Bayesian inference for standard a few one- and two-parameter models, respec- tively. These chapters discuss different types of priors and posterior distributions to perform inferences, and the use of predictive distributions. The conjugate priors-posteriors as well as the posteriors that do not have well-known functional forms, requiring the calculations to be done on a grid of points (by brute-force) to elicit meaningful summaries are covered. Chapter 5 and 6 are the crux of the book, they are concerned with an introduction to mod- ern Bayesian computing. Chapter 5 discusses some of the more complicated computational methods that are employed for the remainder of the book. It covers a multivariate normal approximation to the posterior that serves as a good first approximation in the development of more exact methods. It then provides a general introduction to the use of simulation in computing summaries of the posterior distribution. It describes the rejection sampling al- gorithm in cases where the posterior distribution does not have a standard functional form.
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  • Winter '16
  • Bayesian probability, Bayesian statistics, posterior distribution

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